// SPDX-License-Identifier: EPL-2.0 OR GPL-2.0-or-later
// SPDX-FileCopyrightText: Bradley M. Bell <bradbell@seanet.com>
// SPDX-FileContributor: 2003-22 Bradley M. Bell
// ----------------------------------------------------------------------------

/*
Two old Forward example now used just for valiadation testing
*/

# include <cppad/cppad.hpp>

namespace { // Begin empty namespace

template <class DoubleVector> // vector class, elements of type double
bool ForwardCases(void)
{  bool ok = true;

   using namespace CppAD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) X(2);
   X[0] = 0.;
   X[1] = 1.;
   Independent(X);

   // compute product of elements in X
   CPPAD_TESTVECTOR(AD<double>) Y(1);
   Y[0] = X[0] * X[0] * X[1];

   // create function object F : X -> Y
   ADFun<double> F(X, Y);

   // use zero order to evaluate F[ (3, 4) ]
   DoubleVector x0( F.Domain() );
   DoubleVector y0( F.Range() );
   x0[0]    = 3.;
   x0[1]    = 4.;
   y0       = F.Forward(0, x0);
   ok      &= NearEqual(y0[0] , x0[0]*x0[0]*x0[1], eps99, eps99);

   // evaluate derivative of F in X[0] direction
   DoubleVector x1( F.Domain() );
   DoubleVector y1( F.Range() );
   x1[0]    = 1.;
   x1[1]    = 0.;
   y1       = F.Forward(1, x1);
   ok      &= NearEqual(y1[0] , 2.*x0[0]*x0[1], eps99, eps99);

   // evaluate second derivative of F in X[0] direction
   DoubleVector x2( F.Domain() );
   DoubleVector y2( F.Range() );
   x2[0]       = 0.;
   x2[1]       = 0.;
   y2          = F.Forward(2, x2);
   double F_00 = 2. * y2[0];
   ok         &= NearEqual(F_00, 2.*x0[1], eps99, eps99);

   // evalute derivative of F in X[1] direction
   x1[0]    = 0.;
   x1[1]    = 1.;
   y1       = F.Forward(1, x1);
   ok      &= NearEqual(y1[0] , x0[0]*x0[0], eps99, eps99);

   // evaluate second derivative of F in X[1] direction
   y2          = F.Forward(2, x2);
   double F_11 = 2. * y2[0];
   ok         &= NearEqual(F_11, 0., eps99, eps99);

   // evalute derivative of F in X[0] + X[1] direction
   x1[0]    = 1.;
   x1[1]    = 1.;
   y1       = F.Forward(1, x1);
   ok      &= NearEqual(y1[0], 2.*x0[0]*x0[1] + x0[0]*x0[0], eps99, eps99);

   // use second derivative of F in X[0] direction to
   // compute second partial of F w.r.t X[1] w.r.t X[2]
   y2          = F.Forward(2, x2);
   double F_01 = y2[0] - F_00 / 2. - F_11 / 2.;
   ok         &= NearEqual(F_01 , 2.*x0[0], eps99, eps99);

   return ok;
}

bool ForwardOlder(void)
{  bool ok = true;

   using namespace CppAD;
   using CppAD::NearEqual;
   double eps99 = 99.0 * std::numeric_limits<double>::epsilon();

   // independent variable vector
   CPPAD_TESTVECTOR(AD<double>) U(3);
   U[0] = 0.; U[1] = 1.; U[2] = 2.;
   Independent(U);

   // compute sum and product of elements in U
   AD<double> sum  = 0.;
   AD<double> prod = 1.;
   size_t i;
   for(i = 0; i < 3; i++)
   {  sum  += U[i];
      prod *= U[i];
   }

   // dependent variable vector
   CPPAD_TESTVECTOR(AD<double>) V(2);
   V[0] = sum;
   V[1] = prod;

   // V = f(U)
   ADFun<double> f(U, V);

   // use ADFun object to evaluate f[ (1, 2, 3)^T ] -----------------
   CPPAD_TESTVECTOR(double) u0( f.Domain() );
   CPPAD_TESTVECTOR(double) v0( f.Range() );
   size_t p;
   p     = 0;
   u0[0] = 1.; u0[1] = 2.; u0[2] = 3.;
   v0    = f.Forward(p, u0);

   // direct evaluation of f[ u0 ]
   CPPAD_TESTVECTOR(double) f0(2);
   f0[0] = u0[0] + u0[1] + u0[2];
   f0[1] = u0[0] * u0[1] * u0[2];

   // compare values
   ok &= NearEqual(v0[0] , f0[0], eps99, eps99);
   ok &= NearEqual(v0[1] , f0[1], eps99, eps99);

   // use ADFun object to evaluate f^(1) [ u0 ] * u1 -----------------
   CPPAD_TESTVECTOR(double) u1( f.Domain() );
   CPPAD_TESTVECTOR(double) v1( f.Range() );
   p     = 1;
   u1[0] = 1.; u1[1] = 1.; u1[2] = 1.;
   v1    = f.Forward(p, u1);

   // direct evaluation of gradients of components of f
   CPPAD_TESTVECTOR(double) g0(3), g1(3);
   g0[0] =          1.; g0[1] =          1.; g0[2] =          1.;
   g1[0] = u0[1]*u0[2]; g1[1] = u0[0]*u0[2]; g1[2] = u0[0]*u0[1];

   // compare values
   ok &= NearEqual(v1[0] ,
      g0[0]*u1[0] + g0[1]*u1[1] + g0[2]*u1[2] , eps99, eps99);
   ok &= NearEqual(v1[1] ,
      g1[0]*u1[0] + g1[1]*u1[1] + g1[2]*u1[2] , eps99, eps99);

   // use ADFun object to evaluate ------------------------------------
   // (1/2) * { f^(1)[ u0 ] * u2 + u1^T * f^(2)[ u0 ] * u1 }
   CPPAD_TESTVECTOR(double) u2( f.Domain() );
   CPPAD_TESTVECTOR(double) v2( f.Range() );
   p     = 2;
   u2[0] = .5; u2[1] = .4; u2[2] = .3;
   v2    = f.Forward(p, u2);

   // direct evaluation of Hessian of second components of f
   // (the Hessian of the first component is zero)
   CPPAD_TESTVECTOR(double) H1(9);
   H1[0] =    0.; H1[1] = u0[2]; H1[2] = u0[1];
   H1[3] = u0[2]; H1[4] =    0.; H1[5] = u0[0];
   H1[6] = u0[1]; H1[7] = u0[0]; H1[8] =    0.;

   // compare values
   ok &= NearEqual(v2[0] ,
      g0[0]*u2[0] + g0[1]*u2[1] + g0[2]*u2[2] , eps99, eps99);

   size_t j;
   double v2_1 = 0.;
   for(i = 0; i < 3; i++)
   {  v2_1 += g1[i] * u2[i];
      for(j = 0; j < 3; j++)
         v2_1 += .5 * u1[i] * H1[i * 3 + j] * u1[j];
   }
   ok &= NearEqual(v2[1], v2_1, eps99, eps99);


   return ok;
}

# ifndef NDEBUG
# ifndef CPPAD_DEBUG_AND_RELEASE
void my_error_handler(
   bool known           ,
   int  line            ,
   const char *file     ,
   const char *exp      ,
   const char *msg      )
{  // error hander must not return, so throw an exception
   std::string message = msg;
   throw message;
}

bool forward_nan(void)
{

   using CppAD::vector;
   using CppAD::AD;

   size_t n = 2, m = 1;
   vector< AD<double> > a_x(n), a_y(m);
   a_x[0] = 1.;
   a_x[1] = 2.;
   Independent(a_x);
   a_y[0] = a_x[0] / a_x[1];
   CppAD::ADFun<double> f(a_x, a_y);
   //
   vector<double> x(n), y(m);
   x[0] = 0.;
   x[1] = 0.;

   // replace the default CppAD error handler
   CppAD::ErrorHandler info(my_error_handler);

   bool ok = false;
   try {
      y    = f.Forward(0, x);
   }
   catch( std::string msg )
   {  // check that the message contains
      // "vector_size = " and "file_name = "
      ok = msg.find("vector_size = ") != std::string::npos;
      ok = msg.find("file_name = ") != std::string::npos;
   }

   return ok;
}
# endif
# endif
} // END empty namespace

# include <vector>
# include <valarray>
bool Forward(void)
{  bool ok = true;
   ok &= ForwardCases< CppAD::vector  <double> >();
   ok &= ForwardCases< std::vector    <double> >();
   ok &= ForwardCases< std::valarray  <double> >();
   ok &= ForwardOlder();
# ifndef NDEBUG
# ifndef CPPAD_DEBUG_AND_RELEASE
   // CppAD does not check for nan when NDEBUG is defined
   ok &= forward_nan();
# endif
# endif
   return ok;
}
